Quantum batteries aim to exploit collective and coherent quantum effects to enhance energy storage and charging performance. In this context, the Dicke model provides a paradigmatic platform in which an ensemble of two-level systems interacts collectively with a single cavity mode, potentially enabling superlinear scaling of the charging power. Here, we present a controlled numerical comparison between a collective Dicke quantum battery and a parallel, non-collective benchmark composed of independent two-level systems charged by separate cavity modes. By simulating the open-system dynamics using Lindblad master equations, we analyze the stored energy, optimal charging time, and average charging power as functions of the system size. We identify a clear crossover from superlinear to linear scaling of the charging power controlled by dissipation: collective advantages persist only when coherent light--matter coupling dominates over losses, approximately when $g \gtrsim \kappa + \gamma$. These results delineate the operational regimes in which collective quantum batteries can outperform non-collective architectures and clarify the limitations imposed by environmental decoherence.